Zuko hated board games. He hated all games, including cards, dice, and anything involving tiles. They left a bad taste of tea in his mouth.
Katara loved games. Water tribe women were always working with their hands, but their minds were kept sharp through the endless winter by countless word games of deductive reasoning and persuasion.
Aang loved to play, but his games were all active, and most involved air bending. Although Katara didn't like to disappoint him, his ways were still too childish to keep her entertained.
Which is why she was so surprised to find Zuko, sitting by himself, swearing in three languages while he bounced a tiny red ball against the dirt. "Zuko, what are you doing?"
He replied without looking up, "Shhh, Katara, please. The Avatar is teaching me a meditative training exercise he learned from the monks. It requires great dexterity and concentration. The ball is my inner sun, and these metal x-shaped things are wisdom. I must practice learning to control my inner sun, so I can gather wisdom with increasing speed. My objective is to bounce the ball once with my right hand, use the same hand to scoop up 10 pieces of wisdom, and catch the ball before it falls again. Then I will be worthy to meditate with the Avatar."
This gave Katara a whole new appreciation of Zuko's relationships with his father and sister.
"We have a similar exercise in the water tribe. It purifies the mind of disturbing thoughts, and brings great spiritual clarity," she stated. Zuko said that he'd be honored to learn her tribal traditions. "But you have to promise me, Zuko - once start, you will finish. No matter how difficult it is. I need to trust you." Zuko stood up and looked determined, "Katara, I never give up."
Ten minutes later, he was up to his elbows in warm water, following her instructions to, "cleanse the heavy remains of long journeys from Sokka's socks, and imagine your troubles floating away with the soap."